imc

Question

An architect is building a structure that will place vertical pillars at the vertices of regular hexagon ABCDEF, which is lying horizontally on the ground. The six pillars will hold up a flat solar panel that will not be parallel to the ground. The heights of pillars at A, B, and C are 12, 9, and 10 meters, respectively. What is the height, in meters, of the pillar at E?

Accepted Answer

The pillar at B has height 9 and the pillar at A has height 12. Since the solar panel is flat, the inclination from pillar B to pillar A is 3. Call the center of the hexagon G. Since CGBA, it follows that the solar panel has height 13 at G. Since the solar panel is flat, the heights of the solar panel at B,G, and E are collinear. Therefore, the pillar at E has height 9+4+4=17.